(1) WARP DRIVE FOR SPACE TRAVELTOPJohn
Cipolla is performing unique research in the area of gravitational
warp drive
technology and gravity control for faster than light star travel. The
illustrations below show a spacecraft being accelerated
while enclosed within an artificially generated warp bubble.The following results from
the theory of General Relativity illustrate how
a warp bubble uses opposing regions of expanding
and contracting spacetime for propelling a starship at velocities exceeding
the speed of light. This is a work in progress based on
a new method for warping spacetime to generate warp
bubble disturbances without the need for exotic matter
or negative energy. Experiments are being conducted to
evaluate the method's capability for generating the
theoretical warp metrics depicted in Figure-2, Figure-3, Figure-4
and Figure-5.

Figure-1: Warp bubble traveling
adjacent to the Earth (not to scale)

Figure-2: Warp bubble geometry illustrating
how spacetime compression and expansion
propel a warp bubble and an enclosed starship through space to
distant stars

GENERAL RELATIVITY AND WARP DRIVE THEORYThisRelativisticWarp drive theory uses the
concept of a warp bubble to avoid violating the
universal speed limitation which is the speed of light, c.
Basic to the study of General Relativity is the concept of spacetime curvature embodied bythe following
statement, "Matter-energy tells spacetime how to curve and spacetime tells
matter-energy how to move". The concept of spacetime curvature
is summarized in the Einstein equation which is a result of
the theory of General Relativity. According
to the Einstein equation, matter and energy tell spacetime
how to curve and in turn spacetime tells matter and energy
how to move. Where, matter and energy are defined by the
stress-energy tensor (T) and spacetime curvature is defined
by the Riemann curvature tensor (R). In summation, the
Einstein equation relates spacetime curvature and
accelerated motion of a matter-energy system and the
implication that accelerated motion and the effects of
gravity are not distinguishable. Hence, artificial gravity
can be created by simply rotating a spacecraft to create the
effect of gravity on long journeys into space and a warp
bubble can be used to travel to distant places at many times
the speed of light without locally exceeding the speed of light
in the warp bubble.
WARP BUBBLE PHYSICS
According to General Relativity gravity and acceleration are not
distinguishable and are caused by the curvature or warp metric of
spacetime.
A warp bubble is a specific warp metric solution of General
Relativity and is a combination of positive and negative energy
fields that pushes and pulls our starship forward to bring our
destination to us just like a conveyer belt. The exotic ingredient required to make a warp
bubble is negative energy which has the unusual property of
being able to make ordinary matter fall up in a gravitational
field. According to General
Relativity the spacetime in front of a warp bubble is
compressed pulling our destination to us. At the same time the spacetime behind a warp bubble is expanding pushing us to our
destination. The compression and expansion process happens in an instant and at many times
the speed of light making faster than light travel possible. The
combination of positive and negative energy produces an
expansion of space behind the bubble and a contraction of space
in front of the bubble. in other words, creating space behind the bubble pushes us to our destination
and destroying space in front of the bubble pulls us to our destination.
This mechanism allows us to travel many times faster than the
speed of light (see Starship Warp Velocity) relative to the
Earth without exceeding the speed of light in our local frame of
reference, the warp bubble. The warp bubble itself is made of fields of positive energy at
either end and a band of negative energy around the middle.
These energy fields create huge gravitational effects so powerful the
warp bubble can distort spacetime without having to accelerate
the traveler to achieve faster than light velocity. The main requirement,
negative energy also called vacuum energy is a property of a vacuum where subatomic
particles smaller than an atom dart into and out of existence
almost instantaneously. According to the rules of quantum mechanics
negative energy creates a negative quantum pressure that
propels the warp bubble and therefore our starship forward. An
interesting observation is that we may already see the effects
of negative energy because astronomers have observed that our
universe is expanding due to the presence of dark energy. It is
theorized that dark energy fills the vacuum of space between the
galaxies and is the cause for the expansion and increasing
acceleration of the universe.
Therefore, dark energy and negative energy are probably the same
"stuff" required to make a warp bubble possible.

General Relativity states the equivalent mass-energy of a planet
the size of Jupiter is required to create a warp bubble. Because
producing negative energy is beyond our capability the objective
of this research is to find an alternate way to create a
relativistic warp bubble without the need for exotic matter or negative
energy. It is proposed that a replacement for negative energy
may be possible by using positive energy in unique ways to generate an energy signature
equivalent to the Alcubierre warp metric displayed in
Figure-11 of the RESULTS TO DATE
section.

Figure-9: MathCAD
warp bubble analysis of a hypothetical flight to a star 4.3 light years away

REFERENCES FOR
GENERAL RELATIVITY
Gravitation, Charles W. Misner, Kip S. Thorne and John
A. WheelerSPACETIME and GEOMETRY An Introduction to General
Relativity, Sean M. CarrollRelativity Demystified, David McMahon

These results compare
the warp signature of spacetime generated using frame dragging
as displayed in Figure-3 and Figure-4 to the warp signature
of the Alcubierre warp metric
displayed in Figure-11 and Figure-12. Work continues using a laser to map
spacetime around the experimental warp metric, clocks
to measure time dilation within and around the warp
bubble and force measurements to determine inertia effects.

Laser
experiment used to map spacetime around the
proposed warp drive demonstration device. This laser
measurement system is mechanically and acoustically isolated
from the system used to warp spacetime. Similar experiments
are being designed using synchronized clocks to measure time
dilation effects. No positive results to date.

The same experiment
using fog to trace a laser beam around the warp
bubble disturbance. The laser beam was not deflected
indicating spacetime is not being warped to any
measurable degree by the proposed warp generator. Several
configurations of the warp generator resulted in the same
null result. The experiments are continuing using
conventional energy sources to affect spacetime.

The aim of these experiments
is an attempt to
show that a warp bubble may be generated using
electromagnetic energy instead of negative energy as required by Alcubierre's
faster than light warp metric. The method proposed here to warp
spacetime
theoretically generates a warp bubble (Figure-3) that
superficially matches the signature warp bubble (Figure-1) predicted using negative energy.
General Relativity, Dark Matter and Dark
Energy cosmology indicate that a warp bubble is analogous to
expanding spacetime observed to occur between distant
galaxies. In
effect, expanding spacetime between galaxies is like a
conveyer belt pushing galaxies apart at a rate of approximately
71 km/sec/mega parsec. While measuring the warp effect
predicted by this method has not proven successful the paper
by Alcubierre states the following, "The need for exotic
matter therefore doesn't necessarily eliminate the
possibility of using spacetime distortion like the one
described here for hyper-fast interstellar travel."

This
experiment is an attempt to determine if the inertial
mass
of a 15.5 gram cylindrical aluminum object is reduced within
a proposed gravitational warp bubble. The warp
chamber illustrated in Figure-14 is composed of a ring of
six ceramic magnets that rotate at 1720 RPM. Experiments
conducted using the force balance system illustrated in
Figure-14 has so far not detected any measurable reduction
in the weight or inertial mass of the cylindrical aluminum object. These
experiments will continue using improved force measurement
devices and various orientations as these valuable resources become available ...

The theoretical basis for the
operation of this experiment is that a massive object causes
spacetime to curve and in-turn spacetime tells a
massive object how to move and accelerate. It is postulated
here that spacetimecurvature can be modified
using powerful electromagnetic fields
to reduce the inertial mass of a starship. In the
weakest implementation of this theory a starship can be made
to accelerate as if the inertial mass of the starship were
reduced making near light speed possible using simple
electric thrusters. However, in the most advanced
implementation of this experiment when the energy of the
electromagnetic fields cause the inertial mass of a starship
to become imaginary the starship in the warp
bubble will become a tachyon capable of moving
faster than the speed of light. In its advanced form the
object in the warp bubble is isolated from the rest of the
universe allowing the warp bubble to become a local frame of
reference where Faster Than Light (FTL) travel does
not violate the local speed of light (c).

Tachyon: A particle postulated to move at a velocity
greater than the speed of electromagnetic radiation, such
that as the particle accelerates it loses energy. Of the two
properties rest mass and energy, one must be
real and the other imaginary. If a tachyon
exists it may be detected through the emission of
Cerenkov radiation (a kind of electromagnetic shock wave) or by cosmic
ray collisions.

Positive test
results have been achieved in recent tests "indicating" that
a warp bubble based on free vortex theory can be generated and that propulsion using
these methods may be possible. However, these results have not
been confirmed to be purely a consequence of spacetime
warping or an electro-magnetic effect so further
experimentation is necessary. A new load cell and data
acquisition system made it possible to "tease out" very
small reductions of test item gravitational force. A totally new
configuration not represented by Figure-15 or Figure-18 and
a slight change in methodology made these results possible.

DISCUSSION:
According to the well tested and validated Theory of
General Relativity,gravity
is a direct result of the curvature of spacetime caused by
the presence of mass and energy. It has been proven by observation
of gravitational lensing around
massive objects that mass
and energy warp the fabric of spacetime. The warping of
spacetime by massive objects is a scientific fact where
General Relativity accurately predicts the deflection of
visible light around massive objects like stars, clusters of
stars and galaxies. The fact that mass-energy warps
spacetime has been proven by
Gravity Probe-B (GP-B) a NASA spacecraft that validated Eienstein's 4-dimensional Theory of General
Relativity. The NASA probe proved that higher dimensional
gravitational theories, M-Theory (superstrings) and quantum
mechanics
are
not required for warping spacetime. In addition, very
complex theories are probably not correct because as
Occam's razor states the theory that makes the fewest
assumptions is probably correct. Because General Relativity
is the "simplest" explanation for gravity and because
experiments have proven that gravity is a physical
effect caused by the presence of mass and energy it seems
reasonable that gravity can be controlled and manipulated by
mass and energy in a laboratory experiment. It is not a
theory that 4-dimensional spacetime exists. Therefore,
M-Theory which
has not been proven by a single experiment and quantum mechanics
should not be
required to manipulate the physical large scale
aspects of spacetime and gravity. For example, it is well
known that rotating masses like binary stars and rotating
beams generate gravitational waves in spacetime.

PLASMA WARP CORE EXPERIMENTRESULTS (12/17/2014
to PRESENT)

A rotating
plasma analogous to the inertial mass reduction
experiment that used a rotating magnet has been fabricated to
document the influence a rotating plasma generated
electro-magnetic field has on the
metrics of space-time. The beam of a Helium Neon laser
has been used to penetrate the warp core region of a rotating plasma
core with no deflection observed to date. The challenge has
been to accurately measure laser beam deflection. This experiment is important
because a laser beam is capable of penetrating the
interior of the warp core region without outside
influence. The experiment is considered successful if the laser beam
deflects by even the smallest amount indicating warped
space-time. More images of the
experiment will be posted as the experiments proceed.

ESTABLISHING THE ANALOGY
BETWEEN
GENERAL RELATIVITY AND POTENTIAL VORTEX FLOW
AND RUDIMENTARY WARP DRIVE PROPULSIONBY JOHN CIPOLLA (1990 to 2015)
NEW PAPERS AVAILABLEBy John R. Cipolla,
Copyright 2015

Research has
shown that an analogy exists between potential vortex flow
and the generation of space-time curvature around massive
objects as predicted by Einstein’s theory of General
Relativity (GR). The analogy between GR and potential vortex
flow is based on results from potential vortex
experimentation, GP-B researcher statements, free-surface shape extracted from Schwarzschild’s metric, a
unit analysis of the curvature and energy-momentum
components of potential vortex flow and the analogous
components from Einstein’s Field Equations and black hole
dynamics compared to potential vortex dynamics. Predictions
based on this research
are made that indicate gravity control and rudimentary warp
drive is possible.

An implication for the existence of a superfluid potential vortex substratum is that interesting
fluid mechanical characteristics of space-time can be
revealed. Specifically, an interesting by product of a
superfluid substratum is the Magnus effect. The Magnus
effect is the force exerted on a rapidly spinning cylinder
or sphere moving through air or another fluid in a direction
at an angle to the axis of spin. The sideways force is
responsible for the swerving of balls when hit or thrown
with spin. For example, if an object composed of
energy-momentum rotates in the gravitational field of
another massive object a Magnus effect based on
the superfluid of space-time will impart a sideways force on
the object and an associated acceleration in the substratum.
In exactly the same way the surrounding fluid is deformed by
a spinning object, space-time will be compressed on one side
of the object and expanded on the other side of the object
generating an imbalance in space-time. The deformed
space-time surrounding the spinning object could be called a
warp bubble that uses the imbalance within space-time to
propel an object perpendicular to the field lines of the
surrounding superfluid. Speeds approaching the speed of
light are not practical but exotic materials are not
required for a device based on this technology. The
analogous Magnus effect in General Relativity that uses the
principals of fluid mechanics to model
space-time around a circular cylinder with circulation is
defined as a uniform flow plus a doublet plus a
vortex.

Rotating
mass-energy and resulting warped space-time (3)

Superfluid warp drive operating
in the Solar System (3)

Superfluid vortex
experiment (1, 2)

4-d space-time
interpreted by
GP-B as the surface of a
superfluid.
See
Gravity Probe-B (GP-B) for information

Figure-18: Magnetic field analogy for a
gravity wave generator to determine distant particle motion.
Vector,
V illustrates the motion and velocity of a cylindrical steel mass
exposed to a rotating pair of magnets.
The steel mass is exposed to the quadrupole moment generated by the
rotating pair of ceramic magnets.
The mass follows an elliptical orbit that is perpendicular to the axis of
the rotating pair of magnets.

GRAVITATIONAL WAVES: The law of
gravitation is an inverse square law relationship as
are the laws relating the forces associated with monopole
static charges and dipole magnetism. In general the inverse
square law relates the intensity of a field effect to the
reciprocal of the square of the distance from the source of
the effect. The experiment illustrated in Figure-18 uses a
magnetic field analogy of a gravity wave generator to
demonstrate the effect quadrupole gravitational waves
have on spacetime and particle motion.

To demonstrate that dipole magnetic fields obey an inverse
square law relationship and therefore are a useful mechanism
to visualize quadrupole gravitational radiation for rotating
systems, Figure-16 demonstrates how force verses distance were
experimentally determined to generate the magnetic force
verses distance data presented in Figure-17. As expected
from field theory, dipole magnetism obeys the inverse square
law relationship. The following equation fits the force
verses distance data measured using the method illustrated
in Figure-16 where the relationship is F = C/r^2 and
C = 1.786E5 dyne*mm^2. Because dipole magnetism
obeys the inverse square law it can be assumed the experiment
illustrated in Figure-18 is a reasonable analogy for the
gravity wave generator presented in Figure-19 where several
masses possessing mass and energy are rotated at
high speed. During operation the cylindrical mass in Figure-18 follows a
highly elliptical orbit indicating the presence of an
external magnetic quadrupole field. Therefore, to understand
how gravitational quadrupole radiation affects particle
motion the rotating magnetic field experiment in Figure-18
is useful.

It is well known and documented in GRAVITATION
and other books
about general relativity that rotating systems like binary stars, black holes
and all rotating massive objects generate
gravitational waves due to the reduced quadrupole moment
of the rotating disturbance. Figure-18 illustrates how a
massive rotating system analogous
to a binary star generate
gravitational disturbances in spacetime. Gravity waves are
generated by a rotating mass-energy system because the
differential arrival time from opposite sides of the system
cause a phase angle between gravitational vectors. Gravitational vectors from opposite sides of a
rotating system that initially oppose each other when the
system is stationary are drawn inclined at phase angle, dq
during rotation. The amplitude of the resulting
gravitational wave generates a reduced quadrupole moment
that when squared is proportional to the generated
gravitational power. Further, it can be
shown that like electromagnetic waves, gravitational waves
have energy, U that delivers
momentum, p to a point in spacetime causing a small net force,
F to act at that point. The force, F is the net
gravitational wave force this research is attempting to
generate, enhance and measure.

Figure-22 presents a simple gravitational-wave analysis of a binary star. This example is similar to the example
displayed in GRAVITATION on pages 979 and 980 where the gravitational-wave power output of a massive rotating beam
is computed when the beam rotation frequency is determined
by balancing centrifugal force and beam material tensile
strength. The power radiated in the form of gravitational
waves by the rotating beam is only 2.27E-22 ergs/sec and the force
imparted to an area 500 meters away is only 1.89E-42
newtons. However, if the mass or the rotation rate of
the beam are greatly increased possibly to speeds
approaching the speed of light then a form of gravity
propulsion may be possible. In ways similar to Alcubierre's
warp metric, gravity waves
produce repeated regions of compressed spacetime followed
immediately by regions of expanded spacetime.

WHAT RADIATES GRAVITATIONAL WAVES: In applying the
equations that appear in Figure-20 and Figure-21 one must be
careful to ignore internal power flows that cannot radiate
gravitationally, that is internal motions that do not
accompany a time changing quadrupole moment. For example, a
normal star does not radiate gravitational waves because the
internal power flows associated with spherical pulsation and
axially symmetric rotation are not unbalanced motions.
However, dynamic astrophysical systems that do radiate
gravitational waves include stars that pulsate and rotate
wildly, collapsing stars, exploding stars, feeding black
holes and chaotic systems of stars.

GRAVITY WAVE PROPULSION - HYPOTHESIS:
The power output by a laboratory sized gravitational-wave
generator is very small unless the rate of rotation or the
mass of the beam is greatly increased. However, it is hypothesized
that if the ordinary mass-energy of a rotating beam
is increased to that of the planet Jupiter and if the
rate of rotation is kept the same at 4.456 revolutions per
second it may be possible to impart a force of 28.5 newtons
to an object 500 meters away. Please see Figure-21 for the
basic methodology required for carrying out this analysis.
However, achieving the mass-energy density for
successfully conducting this experiment does not yet exist
on the planet Earth. But, it is encouraging that negative
energy of the same density is not be required.

FURTHER INVESTIGATION: Using the reduced quadrupole
moment of rotating systems deserves further investigation.
For example, the theoretical warp bubble illustrated in
Figure-3 was created using frame dragging and
not negative energy as required by Alcubierre's
warp bubble. While the
theoretical warp bubble illustrated in Figure-3 looks
similar to the negative energy warp bubble illustrated in
Figure-1 and Figure-2 the frame dragging warp bubble needs
to be more clearly understood to determine its true
physical characteristics.

Figure-22: More precise method to
determine gravitational power radiated by a binary star from
GRAVITATION

(2) GRAVITY AND CURVATURE OF SPACETIME
TOPAccording to Einstein's
General Theory of Relativity gravitation is a
manifestation of the curvature of spacetime. Light and
particles of matter travel along geodesics while the geometry
in
which travel occurs takes place in spacetime not just
space. A geodesic is the shortest line between two
points that lies in a given surface. In curved space two
separate geodesics that start off parallel will
eventually cross or intersect. Because gravity is a
manifestation of geometry this behavior will occur in
the motion of particles on geodesics in spacetime. The
intersection of initially parallel geodesics is an
expression of gravitational tidal effects while
traveling within a gravitational field. For example, two
particles in free fall in a gravitational field will
initially move parallel to each other as they approach
the ground. However, because the particles are moving on
radial paths to the center of the massive object they
will seem to move toward each other if the distance
traveled is great enough. This is a description of the
tidal effects of gravity and the spacetime effect on
particles moving in spacetime. This phenomenon is also
called geodesic deviation.

Figure-2 represents the gravitational field determined
using the Schwarzschild metric solution for the
curvature of spacetime outside any spherically
symmetric mass like the Earth, Sun or a black hole. The
tidal effects of gravity on a volume of space as the
volume approaches a massive object is displayed. Changes
of space-extension or distortion of the volume is caused by the
curvature of spacetime.

Figure-2, Volume entering the gravitational field of an object
modeled by the Schwarzschild solution

Furthermore,
the curvature of spacetime causes the path of a light ray
to bend in the region around a massive object. A ray of
light as it approaches the gravitational charge of a massive
object undergoes a deflection through the angle, Fwhen the separation distance, D
is small enough. Using the Schwarzschild metric
solution given by the principle of equivalence the equation
for the deflection angle, Fof a ray of light is illustrated in Figure-3.
Several observations for the deflection of light by the Sun
during solar eclipses are in agreement with this simple
light ray deflection equation.

Figure-3, Deflection of light determined by the Schwarzschild
metric

(3) TEST FOR FLATNESS
OF SPACETIME TOPSometimes it's necessary to
determine the degree to which spacetime is curved. The
following test for spacetime flatness is useful to
determine if the influence of a nearby massive object can be
ignored when trying to determine the relative position of
two particles or two space ships in orbit. The following example
is from page 30 of Gravitation by Misner and Thorne.

Statement of the Problem: A region just above the
surface of the Earth, 100 m x 100 m x 100 m (space
extension) is followed for 10^6 m of light-travel time (T ~
3 seconds). Using the Riemann curvature tensor determine the
uncertainty of measurement for the volume as it traverses
the space around Earth.

Figure-4, Example from Gravitation, page 30

(4) SPACETIME
CURVATURE TOPThe following is a general
method or procedure to determine the non-relativistic
change in the space extension of a volume, region or object
in the vicinity of a massive object caused by tidal effects
of gravity and spacetime curvature. This example is useful
to determine the dimensions of an object as it approaches a
black hole or to determine when spacetime can be considered
Euclidian (flat) or non-Euclidian.

Figure-5, Simple application of the Riemann curvature tensor

(5) GENERAL RELATIVITY THEORY AND APPLICATIONS TOPThe following series of simple
analyses are applications of General Relativity to
the study of Cosmology. Gravity dominates on large scales
making it possible to neglect nuclear and electromagnetic
forces for cosmological approximations. In addition, the
universe is to a very high degree "homogeneous" (the same at
every point) and "isotropic" (the same in every direction) making the spacetime metric nearly the same from one
point to another over large distances. For more information
please see the references especially
Relativity Demystified.

Figure-6, General Relativity theory and applications

6) EFFECTS OF DARK ENERGY ON COSMOLOGY TOPThe cosmology presented here is based on the
concept of dark energy and the resulting negative
pressure required for an expanding universe. These
concepts are important because designing a warp drive
depends on dark energy or something similar to generate
the signature warp bubble required for faster than light
star
travel.

The following are plots of the scale factor (a), Hubble
parameter (H), energy density (r)
and expansion velocity (VH/c) of the universe as a function
of time from the Cosmic Microwave Background which occurred 380,000 years after the
Big Bang. Generating these Cosmology results require the
following equations from Sean M. Carroll's text book, SPACETIME and GEOMETRY
an Introduction to General
Relativity. The equations required for this analysis are: Scale
factor (a), equation 8.183 on page 367, Hubble parameter
(H), equation 8.184 on page 367 and average mass density (r) of the
universe, equation 8.67 on page 336. Equation 8.67 is the Friedmann equation
which relates spacetime curvature (K), mass density and the expansion rate
(H) of the universe. Using the Friedmann equation average mass
density of the universe is determined by substituting K = 0 because the universe is observationally flat
over great distances. Finally, the expansion velocity of the universe is
VH = H*(t/t0)*d,
where t0 is the present time from the CMB and d
is our present distance from the CMB. The CMB
is defined as the Cosmic Microwave Background which occurred
380,000 years after the Big Bang.

Figure-7, Results for scale factor, Hubble
parameter, energy density and expansion velocity of the
universe as
a function of time from when the Cosmic
Microwave Background (CMB) occurred 380,000 years after the
Big Bang

7) UNIFYING GENERAL RELATIVITY AND QUANTUM MECHANICS TOPFirst Published by John
Cipolla April 25, 2012This discussion is an attempt to
unify Einstein's theory of general relativity which governs
gravitational fields around massive objects and quantum
mechanics or the wave nature of matter and energy. String
theory postulates that electrons and quarks in atoms are
one-dimenional oscillating line segments. The first
elementary particle string
models were called bosonic strings because only
bosons or force carriers like photons, gluons and
the Higgs were modeled. Later, superstring
theory was developed that predicted a connection or a "supersymmetry"
between bosons and fermions where fermions are
elementary particles like electrons, protons and quarks that
compose all ordinary matter. This analysis will assume that
massive objects like planets, people and spacecraft are
heterotic (closed) superstrings.

In this case, we are attempting to relate the gravitational
forces predicted by string theory and Einstein's theory of general
relativity. To establish the relationship between general
relativity and quantum mechanics
requires a relatively
simple "model equation" that represents the basic features
of the physics but at a very simplistic level. A "model
equation" for this analysis is required because the full
string theory equations are far too complex for this author
at the present time. This same technique is used in
computational fluid dynamics where solution methods are used
on one-dimensional "model equations" and later extended to
the three dimensional nature of the flow. For this analysis
the one-dimensional string illustrated in Figure-8 represents
the wave equation in Figure-9 and its solution. This is a notional string theory solution not
a
"real" solution. But, the physics of any problem can
sometimes be revealed using this basic technique. The
solution for the wave equation in Figure-9 reveals the
traveling wave velocity of a disturbance on a string
equals the square root of the tension on a string
divided by the linear mass density of the string.

Figure-8, String line segment

Figure-9, Wave equation and the
wave velocity solution for the wave equation

The MathCAD
analysis illustrated in Figure-12 was performed to determine
the gravitational force at the surface of the Earth using
the wave velocity displayed in Figure-9 of the wave equation.
For this analysis the length of the
string is equal to
the circumference of the Earth at the equator and the wave
velocity or traveling velocity of the disturbance in the
string is equal to the velocity of the Earth around the Sun.
According to one interpretation of superstring theory the
heterotic strings of multiple particles merge to eventually
form the massive heterotic string notionally located at the
surface of the Earth. Please see the image on the left which
presents this concept. Following the analysis illustrated in Figure-12 the tension
in the string is analogous to the gravitational force at the
surface of the Earth where the string is notionally located. The
gravitational force predicted by general relativity and
Newtonian mechanics at the surface of the Earth uses the
equation for force (F) and acceleration of gravity (g) expressed in
Figure-10. Comparison using the two methods to determine
gravitational force at the surface of the Earth shows the force predicted by general relativity and Newtonian
mechanics is 43% of the value determined by the simplified
string theory. This difference can be explained by various
factors such as dark matter and dark energy. A difference
of only 43% indicates something fundamental has appeared
which deserves more research. Could missing dark matter be
causing the difference between simplified string theory and general
relativity results?

Figure-10, Gravitational force
predicted by general relativity and Newtonian mechanics

Figure-11, Schrödinger's
equation for a free particle which describes the traveling
wave on a string

Analysis Relating General Relativity
and Simplified String Theory
Figure-12, MathCAD solution of the wave velocity solution of
the
wave equation to estimate gravitational force at the surface
of Earth

Solar
System Analysis: The following graphic plots the
ratio of gravitational potential computed using
general relativity (F) to the gravitational potential
computed by one-dimensional string theory (t).
Notice the wide variation of F/t from planet to planet in the solar
system but average F/t
for the solar system is approximately 1.0 indicating the
over-all correlation between general relativity and string
theory is good. These results indicate gravity can be
modeled as a heterotic string
for a first order approximation of
a grand unifying field theory of gravitation and
quantum mechanics.

REFERENCES FOR
GENERAL RELATIVITY
Gravitation, Charles W. Misner, Kip S. Thorne and John
A. WheelerSPACETIME and GEOMETRY An Introduction to General
Relativity, Sean M. CarrollRelativity Demystified, David McMahonBack to TOP